Timed Shuffle Expressions

  • Cătălin Dima
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3653)


We show that stopwatch automata are equivalent to timed shuffle expressions, an extension of timed regular expressions with the shuffle operation. This implies that the emptiness problem for timed shuffle expressions is undecidable. The result holds for both timed state sequence semantics and timed event sequence semantics of automata and expressions.

Similarly to timed regular expressions, our timed shuffle expressions employ renaming. But we show that even when renaming is not used, shuffle regular expressions still have an undecidable emptiness problem. This solves in the negative a conjecture of Asarin on the possibility to use shuffle to define timed regular languages.


Regular Expression Regular Language Discrete Transition Action Semantic State Symbol 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Cătălin Dima
    • 1
  1. 1.Laboratoire d’Algorithmique, Complexité et LogiqueUniversité Paris XIICréteil CedexFrance

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